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Manipal MET2012MathematicsEllipse

If P is a variable point on the ellipse x^2 a^2 + y^2 b^2 =1 , with A A^ as major axis. Then, the maximum value of the area of the A P A^ is

Options

  1. Aa b sq unit
  2. B2 a b sq unit
  3. Ca b 2 sq unit
  4. DNone of these

Correct answer

A. a b sq unit

Step-by-step solution

The maximum area corresponds to when P is at either end of the minor axis. Required area = 1 2 (2 a) b=a b sq unit

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